Just because you don't understand how something can work doesn't make it ludicrous. People like you are hell bent on destroying what's left of the Earth by turning it into a computer. If we left progress to those without an imagination, we wouldn't even have had a working calculator.
It's the physics of cooling the beasts and the communication delays that make those plans ludicrous.
To turn your assertion on its head, the fact that the supporters don't seem to be able (or willing) to do the math to fact check these proposals is not an indicator that the plans will work.
As a starting point for comparison, the total power budget of the ISS is under 100kW and a single supercomputer rack dissipates about 4x that. What changes to the ISS can be made to get 100x more power and dissipate 100x more heat?
Oh I have done the math. There are multiple ways to get cooling to work in space:
1. There is no real size limit to radiators in space, especially when in solar orbit.
2. High temperature chip architectures can be used, operating at 600K.
3. Heat pipes can bring the temperature even higher, such as to 1200K.
4. Special 3D radiator geometries can be used to optimize heat escape.
5. Metamaterials can be used to optimize photon emission in the best directions.
Together, these will shrink the required radiator area dramatically. Beyond these standard ideas, other exotic approaches exist at the edge of viability.
The ISS in contrast is restricted considering it has to sit in Earth orbit.
You misused a comma; it doesn't belong where you used it.
Just because there are ninety nine ways to do something wrong doesn't mean there couldn't exist one way to do it right. In the case of space datacenters, there absolutely exists a way to do it effectively. Dumb VCs will never know the difference.